Problem: Solve for $x$ and $y$ using elimination. ${-6x+y = -36}$ ${-5x-4y = -59}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $4$ ${-24x+4y = -144}$ $-5x-4y = -59$ Add the top and bottom equations together. $-29x = -203$ $\dfrac{-29x}{{-29}} = \dfrac{-203}{{-29}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-6x+y = -36}\thinspace$ to find $y$ ${-6}{(7)}{ + y = -36}$ $-42+y = -36$ $-42{+42} + y = -36{+42}$ ${y = 6}$ You can also plug ${x = 7}$ into $\thinspace {-5x-4y = -59}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ - 4y = -59}$ ${y = 6}$